Sparks: Succinct parallelizable arguments of knowledge

Abstract

We introduce the notion of a Succinct Parallelizable Argument of Knowledge (SPARK). This is an argument system with the following three properties for computing and proving a time T (non-deterministic) computation:The prover’s (parallel) running time is T + polylog T. (In other words, the prover’s running time is essentially T for large computation times!)The prover uses at most T processors.The communication complexity and verifier complexity are both polylogT. While the third property is standard in succinct arguments, the combination of all three is desirable as it gives a way to leverage moderate parallelism in favor of near-optimal running time. We emphasize that even a factor two overhead in the prover’s parallel running time is not allowed. Our main results are the following, all for non-deterministic polynomial-time RAM computation. We construct (1) an (interactive) SPARK based solely on the existence of collision-resistant hash functions, and (2) a non-interactive SPARK based on any collision-resistant hash function and any SNARK with quasi-linear overhead (as satisfied by recent SNARK constructions).